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  Beyond the Right Answer

  11/12/2026
  Mike Bowler, Head of School
  
  

  Beyond the Right Answer

  Growing the mathematical mind at Harborlight

  
  I can still picture Professor Starr at Amherst College, puzzling over a particularly interesting math problem, chalk smeared around his chin and mouth. As he thought, his hands would travel to his face, leaving traces of the work behind. He was a wonderful, enthusiastic teacher, visibly caught up in the pleasure of exploring an idea.

   

  I wish I had known how to join him in that excitement.

   

  I had arrived at college thinking I was good at math. Throughout school, I could compute quickly, remember procedures, and reliably get the right answer. My teachers noticed, and I enjoyed being seen as a strong math student. I made my way through Calculus in high school and took the next step in that work at Amherst. I even thought I might become a math major.

  But in Professor Starr’s classroom, the familiar rules for success seemed to change. He wanted us to explore the ideas behind the mathematics, consider why something worked, and puzzle through a problem whose path wasn’t immediately clear.

   

  I wanted him to just show me the procedure.

   

  Looking back, I can see how much of my confidence rested on knowing what to do and doing it correctly. My college education had now moved me into abstract mathematics without developing the conceptual understanding that could help me make sense of it. I had learned to follow a path. I was much less comfortable finding one of my own.

   

  And because being “good at math” had become part of my identity, uncertainty felt threatening. What if I couldn’t solve the problem? What would that say about me?

  I earned a B- in that class. I never took another math course.

   

  I return to that experience often as an educator. What would have helped me see an unfamiliar problem as something worth exploring? What experiences might have prepared me to share Professor Starr’s curiosity?

   

  Those questions are part of what makes our mathematics work at Harborlight this year so meaningful to me.

   

  Building on a strong foundation

  One of the things I find most compelling about Montessori mathematics is that conceptual understanding comes first.

   

  Children begin with something they can experience. They hold quantities, compare lengths, compose and decompose numbers, and explore relationships through carefully designed 

  materials. The materials give mathematical ideas a physical form that children can investigate. As their understanding develops, they move toward the symbols and abstractions that represent those ideas.

   

  That foundation is something I was deeply missing in my own education. I could perform procedures, but I did not always understand the mathematics beneath them. Montessori offers children an opportunity to build that understanding from the beginning.

   

  Our responsibility is to attend carefully to how each child makes that journey.
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